Simplify the following expression: $ z = \dfrac{1}{3} - \dfrac{-3k - 3}{-2k} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-2k}{-2k}$ $ \dfrac{1}{3} \times \dfrac{-2k}{-2k} = \dfrac{-2k}{-6k} $ Multiply the second expression by $\dfrac{3}{3}$ $ \dfrac{-3k - 3}{-2k} \times \dfrac{3}{3} = \dfrac{-9k - 9}{-6k} $ Therefore $ z = \dfrac{-2k}{-6k} - \dfrac{-9k - 9}{-6k} $ Now the expressions have the same denominator we can simply subtract the numerators: $z = \dfrac{-2k - (-9k - 9) }{-6k} $ Distribute the negative sign: $z = \dfrac{-2k + 9k + 9}{-6k}$ $z = \dfrac{7k + 9}{-6k}$ Simplify the expression by dividing the numerator and denominator by -1: $z = \dfrac{-7k - 9}{6k}$